All orders asymptotic expansion of large partitions - INSPIRE

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All orders asymptotic expansion of large partitions

Bertrand Eynard
(
- Saclay, SPhT
)

Apr, 2008

39 pages

Published in:

J.Stat.Mech. 0807 (2008) P07023

e-Print:

0804.0381 [math-ph]

DOI:

10.1088/1742-5468/2008/07/P07023

Report number:

SPT-08-056

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Abstract: (arXiv)

The generating function which counts partitions with the Plancherel measure (and its q-deformed version), can be rewritten as a matrix integral, which allows to compute its asymptotic expansion to all orders. There are applications in statistical physics of growing/melting crystals, T.A.S.E.P., and also in algebraic geometry. In particular we compute the Gromov-Witten invariants of the X_p Calabi-Yau 3-fold, and we prove a conjecture of M. Marino, that the generating functions F_g of Gromov--Witten invariants of X_p, come from a matrix model, and are the symplectic invariants of the mirror spectral curve.

References(55)

Figures(0)

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Bertrand Eynard
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Nicolas Orantin
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